Factor $LaTeX: \displaystyle 7 x^{3} - 9 x^{2} - 42 x + 54$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(7 x - 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -6$ , gives $LaTeX: \displaystyle -6(7 x - 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x - 9$ . This gives $LaTeX: \displaystyle x^{2} \left(7 x - 9\right) -6 \cdot \left(7 x - 9\right) = \left(7 x - 9\right) \left(x^{2} - 6\right)$ .